   Chapter 3.3, Problem 45E

Chapter
Section
Textbook Problem

Find the limit. lim θ → 0 sin θ θ + tan θ

To determine

To find: The limit of limθ0sinθθ+tanθ.

Explanation

Limit Laws:

Suppose that c is a constant and the limits limxaf(x) and limxag(x) exist. Then

(1) limxa[f(x)+g(x)]=limxaf(x)+limxag(x)

(2) limxa[f(x)g(x)]=limxaf(x)limxag(x)

(3) limxa[f(x)g(x)]=limxaf(x)limxag(x) if limxag(x)0

Result used:

The value of limθ0sinθθ is 1.

Calculation:

Compute limθ0sinθθ+tanθ.

Divide the numerator and the denominator by θ,

limθ0sinθθ+tanθ=limθ0sinθθθ+tanθθ=limθ0sinθθθθ+tanθθ=limθ0sinθθ1+sinθθcosθ       [

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Solve the equations in Exercises 126. 1x9x3=0

Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 1124, find the indicated limits, if they exist. 15. limx2x+3x29

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

True or False: is a geometric series.

Study Guide for Stewart's Multivariable Calculus, 8th

The length of the curve given by x = 3t2 + 2, y = 2t3, is:

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 